Question

In the figure, two blocks, of mass m1 376 g and m2-558 g, are connected by a massless cord that is wrapped around a uniform disk of mass M 404 g and radius R- 11.3 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension Ti in the cord at the left and (c) the tension T2 in the cord at the right. (a) Num (b) Num (c) Numbe 1.781 UnitsT m/s 2 unte Uni

Answer 1

Given that m_1 = 376 g m_2 = 553 g H = 404 g R = 11.3 cm g = 9.8 m/s^2 Free body diagram: - T_1 - m_1 g = m_1 a T_1 = 3.6848 + 0.376 a, m_2 g - T_2 = m_2 a T_2 = 5.4684 - 0.558 a we know that sigma tau = I alpha rightarrow disc T_2 R - T_1 R = I alpha (5.4684 - 0.558a) - (3.6848 + 0.376 a)R = I alpha I_disc = 1/2 mR^2 therefore alpha = a/R (1.7336 - 0.934 a)R = 1/2 m_3 R^2 times a/R 1.7836 - 0.934 a = 0.5 times 0.404 a a = 1.57 m/s^2 T_1 = 3.6848 + (0.376 times 1.57) T_1 = 4.275 N T_2 = 5.4684 - (0.558 times 1.57) T_2 = 4.592 N